In that sentence, the word like acts as a subordinating conjunction starting the subordinate clause a cigarette should.
This ad campaign raised the ire of grammarians, for they insisted that like is not a subordinating conjunction. The word as, however, is a subordinating conjunction. The word like should not be used as a substitute for as or as if. Thus, they would write the ad:
But in 1866, Charles Darwin wrote:
“Unfortunately few have observed like you have done.” New Fowler, p. 458.
Like as a conjunction meaning “as, in the same way as” (Many shoppers study the food ads like brokers study market reports) or “as if” (It looks like it will rain) has been used for nearly 500 years and by many distinguished literary and intellectual figures.
Since the mid-19th century there have been objections, often vehement, to these uses. Nevertheless, such uses are almost universal today in all but the most formal speech and writing.
In extremely careful speech and in much formal writing, as, as if, and as though are more commonly used than like: The commanding general accepted full responsibility for the incident, as any professional soldier would. Many of the Greenwich Village bohemians lived as if (or as though) there were no tomorrow. Random House, p. 1114.
Every illiterate person uses this construction daily . . . . New Fowler, p. 458.
The Oxford English Dictionary notes that examples of the use of like as a conjunction do appear in the works of “many recent writers of standing” but also points out that such use is “generally condemned as vulgar or slovenly . . . .” Quoted in New Fowler, p. 458.
So restrict your use of like as a conjunction to informal writing or speech. In formal pieces, use as, as if, or as though as proper subordinating conjunctions.
Example: You can act like it doesn’t matter to you, but educated people might respond as if they just met someone needing some grammatical help.
Note: For a thorough discussion of the like word, please read chapter 13 in the Common Grammatical Mistakes section of Grammar.com. Click here for the beginning of that discussion.